Respuesta :

GoddessofDork

So here are a few rules with exponents that you should know:

  1. Multiplying exponents of the same base: [tex] x^m*x^n=x^{m+n} [/tex]
  2. Dividing exponents of the same base: [tex] x^m\div x^n=x^{m-n} [/tex]
  3. Powering a power to a power: [tex] (x^m)^n=x^{m*n} [/tex]
  4. Converting a negative exponent to a positive one: [tex] x^{-m}=\frac{1}{x^m}\ \textsf{and}\ \frac{1}{x^{-m}}=x^m [/tex]

1.

Firstly, solve the outside exponent:

[tex] (2x^3y^7)^{-2}=2^{-2}x^{3*-2}y^{7*-2}=2^{-2}x^{-6}y^{-14} [/tex]

Next, convert the negative exponents into positive ones:

[tex] 2^{-2}x^{-6}y^{-14}=\frac{1}{2^2x^6y^{14}}=\frac{1}{4x^6y^{14}} [/tex]

Your final answer is [tex] \frac{1}{4x^6y^{14}} [/tex]

2.

For this, just divide:

[tex] \frac{12x^5y^3}{4x^{-1}}=\frac{12}{4}x^{5-(-1)}y^{3-0}=3x^6y^3 [/tex]

Your final answer is [tex] 3x^6y^3 [/tex]

3.

For this, convert all negative exponents into positive ones:

[tex] \frac{r^{-7}b^{-8}}{t^{-4}w}=\frac{t^4}{r^7b^8w} [/tex]

Your final answer is [tex] \frac{t^4}{r^7b^8w} [/tex]

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